In Havana on June 23, Colombian President Juan Manuel Santos and Timeoleón Jiménez, the leader of Colombia’s largest guerrilla group, the Revolutionary Armed Forces of Colombia (FARC), shook hands on an agreement laying out a roadmap for a UN-monitored ceasefire and disarmament. The ceasefire will go into effect as soon as the parties finish a few pending questions in a 3 1/2-year peace negotiation.

The historic accord sets a 52-year-old conflict on a glide path toward a peaceful end. By the end of the year, the FARC’s 7,000 fighters, plus a similar or greater number of militias and support personnel, should begin a six-month cantonment, demobilization, and disarmament procedure. The FARC will transition to a political party, and will cease to be a “brand name” for national-level political violence.

It’s unlikely that Colombian forces and the FARC will ever again face each other (intentionally) on a battlefield. In fact, it’s likely that, for at least a generation, Colombia will not face any violent political insurgency with “national reach,” or the ability to operate throughout the country.

Colombia will still have violent groups with “regional reach,” though. These will dominate—and compete for control over—ungoverned areas of the countryside and urban slums where the drug trade and other forms of organized crime thrive. Some may have political claims, like the National Liberation Army (ELN), a much smaller guerrilla group, just as old as the FARC, that has not committed fully to negotiations even after years of “talks about talks” with the government.

Other groups won’t be political at all: devoted to moneymaking, they will function as the armed wing of organized crime. Into this category would go groups like the Urabeños or Gaitanistas, drug trafficking armies headed by former mid-level leaders of brutal pro-government paramilitary groups that demobilized in the mid-2000s. Perhaps 10 to 20 percent of demobilized FARC members, tempted by the profits of Colombia’s illegal economies, may join these other groups or form their own small criminal bands.

Even if some of its former members remain active, though, we can expect the FARC—which gets much of its funding from the cocaine trade—to get out of drug trafficking. But this doesn’t mean the end of drug trafficking in Colombia. Nor does it mean the end of other criminal income streams like illicit precious metals mining, human trafficking, or extortion.

The FARC’s exit will disrupt the criminal networks that enrich themselves from these practices. In some parts of the country, this disruption could be more violent than the latter years of the conflict, as new criminal groups rush to fill the territorial and transactional vacuums the guerrillas leave behind. But the criminal networks themselves will prove as resilient as the government absence and endemic impunity that sustain them.

Without the “guerrilla” label, Colombia will find itself confronting a citizen security challenge familiar to Mexico or Central America: hyper-violent groups, regionally but not nationally dominant, seeking to corrupt local state institutions rather than supplant them, and dominating all aspects of everyday life in the areas they control. In these regions, citizens can forget about having safe neighborhoods, a free press, a vibrant civil society, or full exercise of democratic rights.

As Mexico and Central America have found, these “transnational criminal organizations” are harder to fight than traditional insurgencies. A main reason is that they prefer not to fight. They will confront government forces if cornered, but they would much rather corrupt and penetrate institutions like the police, the military, the judiciary, and prosecutors’, mayors’ and governors’ offices, hollowing them out from within and rendering them useless in the effort to curb criminal violence and protect citizens. In Mexico, the result has been bloody battles fought just for control over municipal police forces—battles that hardly get reported on by terrorized local media. In Central America, it has meant police forces operating without the public’s trust and unable to contend with the world’s highest non-war homicide rates.

We can already see the roots of this possible post-accord future in Colombia. Look no further than Buenaventura, a city on the Pacific coast that is Colombia’s busiest port and a busy trafficking corridor. Buenaventura’s neighborhoods are a terrifying patchwork of gang violence, which in recent years added to the country’s vocabulary the horrifying term “casas de pique”—“chop-up houses” where live victims are dismembered while neighbors hear the screams. As there is very little FARC presence within Buenaventura, this may be an early look at post-FARC violence.

But all is not grim. Colombia also shows us how these regional criminal structures should be confronted. Some of the country’s bravest political leaders, judicial investigators, and civil-society experts have correctly identified the problem as more than just the few thousand individuals wearing illegal armed groups’ uniforms and insignia.

In the late 2000s and early 2010s, these investigators uncovered a vast relationship in several parts of the country between Colombia’s paramilitary groups, which funded themselves largely through the drug trade, and narcotraffickers, large landowners, “legitimate” businesses, and government officials, especially the security forces, local governments, and members of the national Congress. The so-called “para-politics” scandal put over one-third of Colombia’s 2006-2010 Congress in jail, on trial, or under investigation.

It also showed that the best way to confront these violent criminal networks is to focus well beyond their “muscle,” the armed groups themselves. Violent organized crime cannot exist without its corrupt ties to the state. Government officials’ support, or acquiescence, is the oxygen that it breathes.

For the United States and other international donors, a post-conflict strategy in Colombia—and an effective effort against transnational criminal networks in Mexico or Central America—must aim to cut off this oxygen supply. Breaking links between criminality and the state must lie at the core of assistance. That would be more effective than shipping more firepower, facilitating more bombing raids, or creating more SWAT units.

An effective post-accord security strategy would recognize that most roads run through the judicial system. Allowed to do their jobs, honest judges, prosecutors, and investigators can shatter links between government and organized crime. “Allowed to do their jobs” means giving them—and the witnesses whose testimonies are crucial—vastly increased physical protection. It means hiring more of them so that their caseloads are manageable. It means giving them the technology they need to manage cases, handle crime scenes, trace financial flows, and identify relationships. And it means giving them the political support they will need as they prosecute some very powerful people in the “legal” political and economic spheres.

It’s not clear, though, that a stronger judiciary is central to Colombia’s post-conflict plans. While U.S. and Colombian officials draft blueprints for increasing security-force presence and coca-plant eradication in FARC-controlled territories, about one-third of Colombia’s 1,100 counties don’t even have their own prosecutor, according to the Bogotá-based judicial think-tank Dejusticia. Plans to address this problem seem sketchy, like sending “justice buses” to travel from county to county. Colombia will need more than that.

We’ve seen some successful recent efforts to break political-criminal links in Latin America, like the para-politics investigations in Colombia and the UN’s innovative International Commission against Impunity in Guatemala (CICIG). (Colombian prosecutor Iván Velásquez, the current head of CICIG, was a principal para-politics investigator.) It may seem odd at first to cite these examples as signposts for how Colombia can guarantee post-conflict security. But it’s not odd at all: it’s central. Governing territory without impunity is the way to guarantee a lasting, secure peace.